Chessboard 2

Donghyuk has a rectangular chessboard. Its rows and columns are numbered from 0. The cell in row $i$ and column $j$ is black when $i+j$ is even and white when $i+j$ is odd. Some cells of the board hold a piece.

Yunho has a very large supply of L-shaped tiles. One tile is three squares, each the size of a board cell, joined as in the picture below.

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Yunho wants to lay tiles on the board under the following rules.

• A tile can be rotated by 90, 180, or 270 degrees.
• One tile must cover three cells of the board.
• Two tiles must not overlap.
• A tile cannot cover a cell that holds a piece.
• The corner cell of a tile, the one that touches both of the other two squares, must cover a black cell.

Write a program that finds the largest number of tiles Yunho can lay.

The first line contains the number of rows $R$ and the number of columns $C$ of the board. ($1 \le R \le 47$, $1 \le C \le 47$)

Each of the next $R$ lines contains one row of the board as a string of length $C$. 'X' is a cell that holds a piece and '.' is an empty cell.

Print the largest number of tiles Yunho can lay.